I would like to dynamically construct a couple of URLs for our SharePoint users to filter down a rather large list view we have. Rather than create a bunch of different custom views, I was wondering if there is a way to just pass some URL arguments to the AllItems.aspx page and have the filter be applied during page load.

I envision maybe create a text box where they can type a question like "DocumentID" and give it a value of "12345" - then have javascript construct an appropriate URL like:

I wouldn't recommend customizing a regular SharePoint view page in this way. You could create another page though outside of the list or library and put a dataview on there that uses the URL input property.